Victims of Lawrence G. Nassar, the Michigan State University physician who sexually abused young women under the guise of medical treatment, would receive $500 million from the university in a settlement that is believed to be the largest ever reached in a sexual abuse case involving an American university.

It dwarfed the size of the settlement reached in the sex abuse scandal at Pennsylvania State University. And it was larger than many of the settlements that followed the child sex abuse crisis in the Roman Catholic Church.

“I think the number being so large sends a message that is undeniable, that something really terrible happened here and that Michigan State owns it,” said John Manly, a lawyer for many of the 332 women who sued the university over abuse by Dr. Nassar. “When you pay half a billion dollars, it’s an admission of responsibility.”

Women who say they were abused by Dr. Nassar still have lawsuits against U.S.A. Gymnastics, the United States Olympic Committee and others, and the settlement with Michigan State could add pressure in those cases. The settlement by Michigan State, a public university that is the state’s largest, also sent a loud warning to other colleges about the potentially devastating cost of ignoring misconduct.

The agreement comes as officials at the University of Southern California are under fire for failing to report a gynecologist who faced allegations of misconduct for decades, and as other colleges find themselves grappling with a growing number of sexual abuse and assault complaints over the last few years. By late Wednesday, officials at U.S.C. said they had received about 85 complaints about George Tyndall, the gynecologist.

“People now know that these scandals can happen at any university, and they need to understand and be prepared for that,” said Thomas Harnisch, director of state relations and policy analysis at the American Association of State Colleges and Universities.

It was uncertain how the settlement would be paid by Michigan State, an institution that has already seen its credit rating downgraded because of the Nassar scandal. On Wednesday, officials at the university did not respond to questions about how it plans to pay, but taxpayers and Michigan State students, officials signaled earlier, are likely to shoulder at least some of the cost. The university is also expected to try to recoup some of its costs from insurance.

The financial toll is only the latest fallout for Michigan State over Dr. Nassar, who worked at the institution for about 20 years, even as women said they made complaints about his conduct to university coaches, trainers or counselors since at least the late 1990s.

Many women said the university enabled Dr. Nassar’s abuse and for years ignored those who came forward with complaints, and top leaders at Michigan State have lost their jobs over the matter, including Lou Anna K. Simon, the president. Michigan’s attorney general is overseeing a criminal investigation into how Dr. Nassar had been permitted to operate at the university for as long as he did. The federal Education Department is investigating the university’s actions. And the F.B.I. is conducting an internal review of what its agents knew about Dr. Nassar’s conduct and when they knew it, Christopher A. Wray, the agency’s director, told Congress on Wednesday.

The settlement was approved by the university’s elected trustees in a conference call on Tuesday night, but final details still had to be handled.

For the women, some of whom shared their stories of abuse in emotional testimony before judges who sentenced Dr. Nassar to more than 100 years in prison, the financial settlement was a step toward healing, but not a fix for systemic failings at Michigan State.

“I hope that our experiences at M.S.U. have opened up the world’s eyes to the suffering that survivors of sexual assault deal with every day,” said Amanda Thomashow, who complained to university officials in 2014 about Dr. Nassar’s conduct. “And I hope that we can change our attitude toward victims. And I hope that our culture shifts from enabling predators to empowering survivors.”

For about 20 years, Dr. Nassar preyed on young women who came to him for medical care at a Michigan State clinic. When some patients claimed abuse, Dr. Nassar insisted he was performing legitimate medical treatment, and university officials allowed him to continue seeing patients.

All the while, Dr. Nassar’s reputation grew. Big Ten athletes sought treatment from him. He traveled abroad with the national gymnastics team. He was on the sidelines during the Olympics. Dr. Nassar’s victims included some of the best gymnasts in the world, as well as local girls who trained after school at a Michigan club.

Many experts said they believed the settlement was the largest involving sex abuse for a university, though there have been higher settlements outside of universities: The Roman Catholic Archdiocese of Los Angeles agreed in 2007 to pay up to $650 million.

Until now, perhaps the biggest university sex abuse settlement was the roughly $109 million related to Jerry Sandusky, an assistant football coach at Penn State who was convicted of abusing boys over 15 years. There were more than 30 plaintiffs in that case. Penn State also paid a $60 million fine as part of a punishment levied by the N.C.A.A. and spent nearly $30 million more over two years on internal legal and investigative costs, according to a 2015 audit. Penn State continues to dispute how much of the payout should be covered by insurance.

In March, John Engler, Michigan State’s interim president, noted Penn State’s ongoing effort to get insurance to cover more of its settlement. Before Michigan legislators, Mr. Engler said that he hoped insurance would cover at least some of Michigan State’s settlement cost, but that students and taxpayers would likely have to cover the rest.

The $500 million settlement would amount to almost 37 percent of the annual general fund budget of $1.36 billion for 2017-18, according to university documents. Of that, almost three-quarters, or $983 million, came from tuition and fees, while state appropriations accounted for a fifth, or $281 million. Michigan lawmakers have capped the amount by which the university can raise tuition. And Michigan State’s endowment is $2.7 billion, but federal law restricts the use of endowments in such situations.

Mr. Harnisch said the money for Michigan State’s settlement would likely come from some combination of insurance, state aid and revenue from student tuition. “They’ll likely have to use reserve funds and borrow money,” he said, “but I think definitely borrowing money is going to be a key piece to paying for this.”

Kenneth Feinberg, the mediator in the Sandusky case at Penn State and the special master of the fund to compensate victims of the Sept. 11 terrorist attacks, said the fact that the parties were able to voluntarily settle the case would help Michigan State rebuild its reputation.

About 10 law firms represented Dr. Nassar’s victims. Mr. Manly, who represents many of the women, did not say how much of the settlement money would go to lawyers in the cases. Each woman will receive just under $1.3 million on average; some will get much more, and others much less, he said.

“It certainly makes sense for Michigan State to try and rebuild and enhance its reputation by quickly resolving all of these claims with these 300 people, without forcing them further damage by litigating,” Mr. Feinberg said. “It makes sense.”

In the months ahead, Michigan State leaders have promised to change policies to prevent future abuse and to begin restoring the university’s tattered reputation. Michael Roach, 73, a 1966 graduate of Michigan State, said he was relieved to learn of the settlement, which he hoped would spare the university from a lengthy lawsuit and troubling media attention.

“It’s bringing some closure, for the survivors and the university,” said Mr. Roach, who plans to continue donating to the college. “If they needed to use my monies” for the settlement, he said, “I guess I would be willing to say, ‘O.K.’”

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Michigan State Agrees to Pay $500 Million to Sex Abuse Victims. Order Reprints | Today’s Paper | Subscribe